Teacher subject matter knowledge for the meaningful transition from arithmetic to algebra

Abstract

Teacher knowledge is particularly important in middle school mathematics to enhance the meaningful transition from arithmetic to algebra. Developing a solid understanding of algebra requires teachers to unpack the meaning underlying the basic concepts, make clear and explicit distinctions among concepts, and facilitate students to connect these concepts with their prior knowledge and understandings in arithmetic. This study focused on the content knowledge (i.e., decompose, trim, and bridge) of three middle school mathematics teachers in practice during the introduction of basic algebra concepts (i.e., variable, algebraic expression, equality and equations). Case study was used as research design in this research. Individual interviews and observations regarding the instructions were used to gather data. Results showed that the participating teachers" conceptions regarding the variable, algebraic expression and equation were rather narrow and it resulted in several constraints when unpacking their meaning in the classroom. While bridging was a commonly observed instructional practice among the participating teachers, the quality of bridging, did not always provide opportunities for a meaningful transition. Trimming, on the other hand, was not observed as a common teaching practice.

Investigation of mathematics teachers teaching practices in transition to algebra in the context of letter symbols

“…In this sense, it is determined that teachers play an important role in the meaning of letter symbols that play a key role in the transition to algebra. On the other hand, while the difficulties experienced by students, their algebraic understanding and algebraic thinking levels are generally discussed in studies (Akkan & Baki, 2016b;Boulton-Lewis et al, 1997;Çelik & Güneş, 2013;Nayıroğlu, 2022;Ursini & Trigueros, 2011), it has been seen that the studies conducted with the teachers are limited in number (Asquith et al, 2007;Baş et al, 2011;Gürsoy, 2019;Yıldız & Yetkin-Özdemir, 2021). For students to overcome their difficulties in learning algebra, it is important for teachers to practice how to teach the subject.…”